Supersymmetry, quark confinement and the harmonic oscillator

TL;DR

This paper explores quantum systems with modified commutation relations involving the Hamiltonian, examining implications for supersymmetry, quark confinement, and harmonic oscillator models, including a relativistic Klein-Gordon-like equation.

Contribution

It introduces a novel class of quantum systems with noncanonical commutation relations linked to the Hamiltonian, extending understanding of supersymmetry and confinement phenomena.

Findings

Analysis of modified commutation relations and their impact on quantum systems

Development of models connecting supersymmetry with quark confinement

Introduction of a Klein-Gordon-like wave equation framework

Abstract

We study some quantum systems described by noncanonical commutation relations formally expressed as [q,p]=ihbar(I + chi H), where H is the associated (harmonic oscillator-like) Hamiltonian of the system, and chi is a Hermitian (constant) operator, i.e. [H,chi]=0 . In passing, we also consider a simple (chi=0 canonical) model, in the framework of a relativistic Klein-Gordon-like wave equation.